Auxetic structures and footwear with soles having auxetic structures

ABSTRACT

A material that includes at least one layer made of an auxetic structure and articles of footwear having soles comprising the materials. When the material is under tension, it expands in both the direction under tension and in the direction orthogonal to the direction under tension. The articles of footwear have soles that have at least one layer made of a material that has a pattern of apertures to provide the auxetic structure. The apertures are surrounded by sole portions that can rotate or pivot to change the size of the apertures. An outer covering can be mated with an outsole structure formed by the auxetic structure. The outer covering includes features that mate with the apertures in the outsole structure. The outer covering is elastic and can stretch to accommodate expansion of the auxetic structure.

CROSS REFERENCE TO RELATED APPLICATION

This application is a divisional of U.S. patent application Ser. No.15/193,319, published as US 2016/0302520, which is a divisional of U.S.Pat. No. 9,402,439. Both references are incorporated by reference intheir entirety.

BACKGROUND

Articles of footwear typically have at least two major components, anupper that provides the enclosure for receiving the wearer's foot, and asole secured to the upper that is the primary contact to the ground orplaying surface. The footwear may also use some type of fasteningsystem, for example, laces or straps or a combination of both, to securethe footwear around the wearer's foot. The sole may comprise threelayers—an inner sole, a midsole and an outer sole. The outer sole is theprimary contact to the ground or the playing surface. It generallycarries a tread pattern and/or cleats or spikes or other protuberancesthat provide the wearer of the footwear with improved traction suitableto the particular athletic, work or recreational activity, or to aparticular ground surface.

SUMMARY

As used herein, the term “auxetic structure” generally refers to astructure that, when it is placed under tension in a first direction,increases its dimensions in a direction that is orthogonal to the firstdirection. For example, if the structure can be described as having alength, a width and a thickness, then when the structure is undertension longitudinally, it increases in width. In certain of theembodiments, the auxetic structures are bi-directional such that theyincrease in length and width when stretched longitudinally and in widthand length when stretched laterally, but do not increase in thickness.Such auxetic structures are characterized by having a negative Poisson'sratio. Also, although such structures will generally have at least amonotonic relationship between the applied tension and the increase inthe dimension orthogonal to the direction of the tension, thatrelationship need not be proportional or linear, and in general needonly increase in response to increased tension.

The article of footwear includes an upper and a sole. The sole mayinclude an inner sole, a midsole and an outer sole. The sole includes atleast one layer made of an auxetic structure. This layer can be referredto as an “auxetic layer.” When the person wearing the footwear engagesin an activity, such as running, turning, leaping or accelerating, thatputs the auxetic layer under increased longitudinal or lateral tension,the auxetic layer increases its length and width and thus providesimproved traction, as well as absorbing some of the impact with theplaying surface. Although the descriptions below only discuss a limitednumber of types of footwear, embodiments can be adapted for many sportand recreational activities, including tennis and other racquet sports,walking, jogging, running, hiking, handball, training, running orwalking on a treadmill, as well as team sports such as basketball,volleyball, lacrosse, field hockey and soccer.

In one aspect, an article of footwear includes an upper and a solestructure. The sole structure includes an outsole, where the solestructure has a first direction that is tangential to an outer surfaceof the outsole and the sole structure has a second direction that isorthogonal to the first direction, where the second direction is alsotangential to the outer surface of the outsole. The sole structurefurther includes a plurality of apertures arranged in geometricpatterns. Tensioning the sole structure in the first direction causesthe outsole to expand in both the first direction and the seconddirection.

In another aspect, a sole structure for an article of footwear includesan outsole having a structure comprised of a pattern of hexagonalpatterns. The outsole defines a plane. The hexagonal patterns comprisepolygonal apertures surrounded by triangular portions joined to eachother by joints that function as hinges allowing the triangular portionsto rotate with respect to each other. When the outsole is under tensionin a first direction, the outsole expands in both the first directionand in a second direction that is orthogonal to the first direction andis in the plane of the sole structure.

In another aspect, an article of footwear includes an upper and a solestructure, where the sole structure comprises an outsole, the outsolebeing characterized by having polygonal portions surrounding polygonalapertures. The polygonal portions are hingedly joined to adjoiningpolygonal portions such that a plurality of the polygonal portionsrotate with respect to each other when the sole structure is undertension. When a portion of the outsole is under longitudinal tension itexpands in both the longitudinal direction and the lateral direction andwhen the portion of the outsole is under lateral tension it expands inboth the lateral direction and the longitudinal direction.

In another aspect, an article of footwear includes an outsole thatincludes a pattern of polygonal apertures formed by triangular portionssurrounding the polygonal apertures. The polygonal apertures have acenter. The triangular portions are joined at their vertices such thatthey function as hinges thereby allowing the triangles to rotate withrespect to each other. The outsole is characterized by having a lateraldirection, a longitudinal direction and a vertical direction. When aportion of the outsole is under lateral tension, it expands in both thelateral direction and the longitudinal direction, and when a portion ofthe outsole is under longitudinal tension it expands in both thelongitudinal direction and the lateral direction. When a portion of theoutsole is under vertical compression, the triangular portions areforced towards the center of the polygonal apertures.

In another aspect, an auxetic structure includes a pattern of polygonalapertures characterized by having at least three reentrant sides andhaving a center. The auxetic structure has a longitudinal direction anda lateral direction and a thickness. Under longitudinal tension theauxetic structure expands in both the longitudinal direction and thelateral direction. Under lateral tension the auxetic structure expandsin both the lateral and longitudinal directions. Under verticalcompression the polygonal apertures collapse towards their centers.

In another aspect, a sheet of material has a longitudinal direction, alateral direction and a vertical direction. The sheet of material alsoinclude a pattern of hexagonal structures having apertures surrounded bytriangular portions, where each triangular portion is joined to anadjoining triangular portion by a flexible joint such that thetriangular portions can rotate with respect to each other. When thesheet of material is under tension in the longitudinal direction itexpands in both the longitudinal direction and the lateral direction.

In another aspect, a composite auxetic material includes a first layerof relatively hard material comprising a pattern of polygonal aperturessurrounded by polygonal portions, where each polygonal portion is joinedto an adjoining polygonal feature by a flexible joint such that thepolygonal portions may rotate with respect to each other when the firstlayer is under tension. The material further includes a second layer ofrelatively resilient material attached to the first layer, where thesecond layer has the same pattern of polygonal apertures as the firstlayer and wherein the pattern of polygonal apertures in the second layeris aligned with the pattern of polygonal apertures in the first layer.When the composite auxetic material is under tension in a firstdirection, it expands in both the first direction and in a seconddirection that is orthogonal to the first direction.

Other systems, methods, features and advantages of the embodiments willbe, or will become, apparent to one of ordinary skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional systems, methods, features andadvantages be included within this description and this summary, bewithin the scope of the embodiments, and be protected by the followingclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments can be better understood with reference to the followingdrawings and description. The components in the figures are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the embodiments. Moreover, in the figures, likereference numerals designate corresponding parts throughout thedifferent views.

FIG. 1 is a schematic diagram of a side view of an embodiment of anarticle of footwear with an example of a sole with an auxetic structure;

FIG. 2 is a schematic diagram of a bottom perspective view of anembodiment of the article of footwear shown in FIG. 1;

FIG. 3 shows a sequence of schematic diagrams of a bottom view of theportion of the outsole of FIG. 1 in various states of tension;

FIG. 4 is a schematic diagram of a top view of an embodiment of anoutsole with the upper removed;

FIG. 5 is a schematic diagram of a bottom view of the outsole shown inFIG. 4;

FIG. 6 is a schematic diagram of an enlarged view of the heel region ofthe outsole shown in FIG. 5 when it is not under tension;

FIG. 7 is a schematic diagram of a cross-section along the line A-Aidentified in FIG. 6;

FIG. 8 is a schematic diagram of an enlarged view of the heel regionshown in FIG. 5;

FIG. 9 is a schematic diagram of an enlarged view of the heel regionshown in FIG. 5 when it is under longitudinal tension;

FIG. 10 is a schematic diagram of an enlarged view of the heel regionshown in FIG. 5 when it is under lateral tension;

FIG. 11 is a schematic diagram of an embodiment of a sole when it is notunder tension;

FIG. 12 is a schematic diagram of an enlarged view of a portion of theforefoot of the sole shown in FIG. 11 when it is under lateral tension;

FIG. 13 is a schematic diagram of an enlarged view of a portion of theforefoot of the sole shown in FIG. 11 when it is under longitudinaltension;

FIG. 14 is a schematic diagram of an enlarged view of a portion of themidfoot of the sole shown in FIG. 11 when it is under longitudinaltension;

FIG. 15 is a schematic diagram of an enlarged view of a portion of themidfoot of the sole shown in FIG. 11 when it is under increasedlongitudinal tension;

FIG. 16 is a schematic diagram of an enlarged view of the forefoot ofthe sole shown in FIG. 5 when it is not under tension;

FIG. 17 is a schematic diagram of an enlarged view of the forefoot ofthe sole shown in FIG. 5 when it is under longitudinal tension;

FIG. 18 is a schematic diagram of an enlarged view of the forefoot ofthe sole shown in FIG. 5 when it is under lateral tension;

FIG. 19 is a schematic diagram of a bottom view of a portion of anoutsole of an embodiment having ground-engaging members when it is notunder tension;

FIG. 20 is a schematic diagram of a cross-section of the sole of theembodiment shown in FIG. 19;

FIG. 21 is a schematic diagram of a top view of a portion of the outsoleof FIG. 19 when it is not under tension;

FIG. 22 is a schematic diagram of a top view of a portion of the outsoleof FIG. 19 when it is under tension;

FIG. 23 shows a sequence of schematic diagrams of a bottom view of theportion of the outsole of FIG. 19 in various states of tension;

FIG. 24 is a schematic diagram of a bottom view of an outsole of anembodiment when it is not under tension;

FIG. 25 shows a sequence of schematic diagrams of a bottom view of theportion of the outsole of FIG. 24 in various states of tension;

FIG. 26 is a schematic diagram of another embodiment of an outsole whenit is not under tension;

FIG. 27 is a schematic diagram of the embodiment of FIG. 26 when it isunder tension;

FIG. 28 is a schematic diagram of a top view of an embodiment of anouter covering that mates with the outsole of FIG. 26;

FIG. 29 is a schematic diagram showing how the outer the covering ofFIG. 28 mates with the outsole of FIG. 26;

FIG. 30 is a schematic diagram of a side perspective view of the outsoleand outer covering of FIG. 28 and FIG. 29;

FIG. 31 is a schematic diagram of is a cross-section of an exemplaryconstruction of a sole bearing the outsole of FIG. 26 and the outercovering of FIG. 28;

FIG. 32 is a schematic diagram of an embodiment of an article offootwear with a knit upper and a sole having an auxetic structure;

FIG. 33 is a schematic diagram of the outsole of the article of footwearof FIG. 32 showing its auxetic structure;

FIG. 34 is a schematic diagram of a side perspective view of the articleof footwear of FIG. 32;

FIG. 35 is a schematic diagram of an enlarged perspective bottom view ofthe heel of the article of footwear of FIG. 32;

FIG. 36 is a schematic diagram of an enlarged view of a midfoot portionof the outsole of the article of footwear of FIG. 32;

FIG. 37 is a schematic diagram of the interior of the article offootwear of FIG. 32;

FIG. 38 is a schematic diagram of a cross-section of the article offootwear of FIG. 32 taken at the forefoot;

FIG. 39 is a schematic diagram of a side view of a running shoe with awoven upper including an auxetic sole structure;

FIG. 40 is a schematic diagram of a bottom view of the outsole of thearticle of footwear of FIG. 39;

FIG. 41 is a schematic diagram of an enlarged perspective bottom view ofthe forefoot region of the article of footwear of FIG. 39;

FIG. 42 is a schematic diagram of an enlarged perspective view of theheel of the article of footwear of FIG. 39;

FIG. 43 is a schematic diagram of a cross-section of the article offootwear of FIG. 39;

FIG. 44 is a schematic diagram of a side view of another embodiment of ashoe with an upper and a outsole having an auxetic structure;

FIG. 45 is a schematic diagram of the interior of the article offootwear of FIG. 44 at the heel region of the shoe;

FIG. 46 is a schematic view of a portion of an outsole with apertures ina non-compressed configuration; and

FIG. 47 is a schematic view of a portion of an outsole with apertures ina compressed configuration.

DETAILED DESCRIPTION

For clarity, the detailed descriptions herein describe certain exemplaryembodiments, but the disclosure herein may be applied to any article offootwear comprising certain of the features described herein and recitedin the claims. In particular, although the following detaileddescription discusses exemplary embodiments, in the form of footwearsuch as running shoes, jogging shoes, tennis, squash or racquetballshoes, basketball shoes, sandals and flippers, the disclosures hereinmay be applied to a wide range of footwear.

For consistency and convenience, directional adjectives are employedthroughout this detailed description corresponding to the illustratedembodiments. The term “longitudinal direction” as used throughout thisdetailed description and in the claims refers to a direction extending alength (or longest dimension) of an article of footwear such as a sportsor recreational shoe. Also, the term “lateral direction” as usedthroughout this detailed description and in the claims refers to adirection extending along a width of an article of footwear. The lateraldirection may generally be perpendicular to the longitudinal direction.The term “vertical direction” as used with respect to an article offootwear throughout this detailed description and in the claims refersto the direction that is normal to the plane of the sole of the articleof footwear.

The term “sole structure”, also referred to simply as “sole”, hereinshall refer to any combination that provides support for a wearer's footand bears the surface that is in direct contact with the ground orplaying surface, such as a single sole; a combination of an outsole andan inner sole; a combination of an outsole, a midsole and an inner sole,and a combination of an outer covering, an outsole, a midsole and aninner sole.

FIG. 1 is a side perspective view of an embodiment of an article offootwear 100. Article of footwear 100 may include upper 101 and solestructure 102, also referred to hereafter simply as sole 102. Upper 101has a heel region 103, an instep or midfoot region 104 and a forefootregion 105. Upper 101 may include an opening or throat 110 that allowsthe wearer to insert his or her foot into the footwear. In someembodiments, upper 101 may also include laces 111, which can be used totighten or otherwise adjust upper 101 around a foot.

In some embodiments, sole 102 includes at least an outsole 120 that maybe the primary ground-contacting surface. In some embodiments, sole 102may also have an inner sole, a midsole, or both an inner sole and amidsole. In some embodiments, outsole 120 may bear a tread pattern, ormay have cleats, spikes or other ground-engaging protuberances.

FIG. 2 is a bottom perspective view of an embodiment of an article offootwear. This figure shows the bottom of outsole 120. Outsole 120 has aheel region 123, an instep or midfoot region 124, and a forefoot region125 as shown in FIG. 2. Outsole 120 has apertures surrounded bypolygonal features that are joined to each other at their vertices. Thejoints at the vertices function as hinges, allowing the polygonalfeatures to rotate as the sole is placed under tension. This actionallows the portion of the sole under tension to expand both in thedirection under tension and in the direction in the plane of the solethat is orthogonal to the direction under tension. Thus, these aperturesand polygonal features form an auxetic structure for outsole 120, whichis described in further detail below.

As shown in FIG. 2, outsole 120 comprises an approximately flat surfacethat includes a plurality of apertures 131, also referred to simply asapertures 131 hereafter. As an example, an enlarged view of firstaperture 139 of apertures 131 is shown schematically within FIG. 2.First aperture 139 is further depicted as having a first portion 141, asecond portion 142, and a third portion 143. Each of these portions isjoined together at a central portion 144. Similarly, in someembodiments, each of the remaining apertures in apertures 131 mayinclude three portions that are joined together, and extend outwardlyfrom, a central portion.

Generally, each aperture in plurality of apertures 131 may have any kindof geometry. In some embodiments, an aperture may have a polygonalgeometry, including a convex and/or concave polygonal geometry. In suchcases, an aperture may be characterized as comprising a particularnumber of vertices and edges (or sides). In an exemplary embodiment,apertures 131 may be characterized as having six sides and six vertices.For example, aperture 139 is shown as having first side 151, second side152, third side 153, fourth side 154, fifth side 155 and sixth side 156.Additionally, aperture 139 is shown as having a first vertex 161, secondvertex 162, third vertex 163, fourth vertex 164, fifth vertex 165 andsixth vertex 166.

In one embodiment, the shape of aperture 139 (and correspondingly of oneor more of apertures 131) may be characterized as a regular polygon,which is both cyclic and equilateral. In some embodiments, the geometryof aperture 139 can be characterized as triangles with sides that,instead of being straight, have an inwardly-pointing vertex at themidpoint of the side. The reentrant angle formed at theseinwardly-pointing vertices can range from 180° (when the side isperfectly straight) to, for example, 120° or less.

Other geometries are also possible, including a variety of polygonaland/or curved geometries. Exemplary polygonal shapes that may be usedwith one or more of apertures 131 include, but are not limited to:regular polygonal shapes (e.g., triangular, rectangular, pentagonal,hexagonal, etc.) as well as irregular polygonal shapes or non-polygonalshapes. Other geometries could be described as being quadrilateral,pentagonal, hexagonal, heptagonal, octagonal or other polygonal shapeswith reentrant sides.

In the exemplary embodiment, the vertices of an aperture (e.g., aperture139) may correspond to interior angles that are less than 180 degrees orinterior angles that are greater than 180 degrees. For example, withrespect to aperture 139, first vertex 161, third vertex 163 and fifthvertex 165 may correspond to interior angles that are less than 180degrees. In this particular example, each of first vertex 161, thirdvertex 163 and fifth vertex 165 has an interior angle A1 that is lessthan 180 degrees. In other words, aperture 139 may have a locally convexgeometry at each of these vertices (relative to the outer side ofaperture 139). In contrast, second vertex 162, fourth vertex 164 andsixth vertex 166 may correspond to interior angles that are greater than180 degrees. In other words, aperture 139 may have a locally concavegeometry at each of these vertices (relative to the outer side ofaperture 139). In this particular example, each of second vertex 162,fourth vertex 164 and sixth vertex 166 may correspond to interior anglesthat are greater than 180 degrees.

Although the embodiments depict apertures having approximately polygonalgeometries, including approximately point-like vertices at whichadjoining sides or edges connect, in other embodiments some or all of anaperture could be non-polygonal. In particular, in some cases, the outeredges or sides of some or all of an aperture may not be joined atvertices, but may be continuously curved. Moreover, some embodiments caninclude apertures having a geometry that includes both straight edgesconnected via vertices as well as curved or non-linear edges without anypoints or vertices.

In some embodiments, apertures 131 may be arranged in a regular patternon outsole 120. In some embodiments, apertures 131 may be arranged suchthat each vertex of an aperture is disposed near the vertex of anotheraperture (e.g., an adjacent or nearby aperture). More specifically, insome cases, apertures 131 may be arranged such that every vertex thathas an interior angle less than 180 degrees is disposed near a vertexthat has an interior angle greater than 180 degrees. As one example,first vertex 161 of aperture 139 is disposed near, or adjacent to, avertex 191 of another aperture 190. Here, vertex 191 is seen to have aninterior angle that is greater than 180 degrees, while first vertex 161has an interior angle that is less than 180 degrees. Similarly, secondvertex 162 of aperture 139 is disposed near, or adjacent to, a vertex193 of another aperture 192. Here, vertex 193 is seen to have aninterior angle that is less than 180 degrees, while second vertex 162has an interior angle that is greater than 180 degrees.

The configuration resulting from the above arrangement may be seen todivide sole structure 120 into smaller geometric portions, whoseboundaries are defined by the edges of apertures 131. In someembodiments, these geometric portions may be comprised of polygonalportions. For example, in the exemplary embodiment, apertures 131 arearranged in a manner that defines a plurality of polygonal portions 200,also referred to hereafter simply as polygonal portions 200.

Generally, the geometry of polygonal portions 200 may be defined by thegeometry of apertures 131 as well as their arrangement on outsole 120.In the exemplary configuration, apertures 131 are shaped and arranged todefine a plurality of approximately triangular portions, with boundariesdefined by edges of adjacent apertures. Of course, in other embodimentspolygonal portions could have any other shape, including rectangular,pentagonal, hexagonal, as well as possibly other kinds of regular andirregular polygonal shapes. Furthermore, it will be understood that inother embodiments, apertures may be arranged on an outsole to definegeometric portions that are not necessarily polygonal (e.g., comprisedof approximately straight edges joined at vertices). The shapes ofgeometric portions in other embodiments could vary and could includevarious rounded, curved, contoured, wavy, nonlinear as well as any otherkinds of shapes or shape characteristics.

As seen in FIG. 2, polygonal portions 200 may be arranged in regulargeometric patterns around each aperture. For example, aperture 139 isseen to be associated with first polygonal portion 201, second polygonalportion 202, third polygonal portion 203, fourth polygonal portion 204,fifth polygonal portion 205 and sixth polygonal portion 206. Moreover,the approximately even arrangement of these polygonal portions aroundaperture 139 forms an approximately hexagonal shape that surroundsaperture 139.

In some embodiments, the various vertices of an aperture may function asa hinge. In particular, in some embodiments, adjacent portions ofmaterial, including one or more geometric portions (e.g., polygonalportions), may rotate about a hinge portion associated with a vertex ofthe aperture. As one example, each vertex of aperture 139 is associatedwith a corresponding hinge portion, which joins adjacent polygonalportions in a rotatable manner.

In the exemplary embodiment, aperture 139 includes hinge portion 210(see FIG. 3), which is associated with vertex 161. Hinge portion 210 iscomprised of a relatively small portion of material adjoining firstpolygonal portion 201 and sixth polygonal portion 206. As discussed infurther detail below, first polygonal portion 201 and sixth polygonalportion 206 may rotate with respect to one another at hinge portion 210.In a similar manner, each of the remaining vertices of aperture 139 areassociated with similar hinge portions that join adjacent polygonalportions in a rotatable manner.

FIG. 3 illustrates a schematic sequence of configurations for a portionof outsole 120 under a tensioning force applied along a single axis ordirection. Specifically, FIG. 3 is intended to illustrate how thegeometric arrangements of apertures 131 and polygonal portions 200provide auxetic properties to outsole 120, thereby allowing portions ofoutsole 120 to expand in both the direction of applied tension and adirection perpendicular to the direction of applied tension.

As shown in FIG. 3, a portion 230 of outsole 200 proceeds throughvarious intermediate configurations as a result of an applied tension ina single linear direction (for example, the longitudinal direction). Inparticular, the four intermediate configurations may be associated withincreasing levels of tension that is applied along a single direction.

Due to the specific geometric configuration for polygonal portions 200and their attachment via hinge portions, this linear tension istransformed into rotation of adjacent polygonal portions 200. Forexample, first polygonal portion 201 and sixth polygonal portion 206 arerotated at hinge portion 210. All of the remaining polygonal portions200 are likewise rotated as apertures 131 expand. Thus, the relativespacing between adjacent polygonal portions 200 increases. For example,as seen clearly in FIG. 3, the relative spacing between first polygonalportion 201 and sixth polygonal portion 206 (and thus the size of firstportion 141 of aperture 131) increases with increased tension.

As the increase in relative spacing occurs in all directions (due to thesymmetry of the original geometric pattern of apertures), this resultsthe expansion of portion 230 along a first direction as well as along asecond direction orthogonal to the first direction. For example, in theexemplary embodiment, in the initial or non-tensioned configuration(seen on the left in FIG. 3), portion 230 initially has an initial sizeD1 along a first linear direction (e.g., the longitudinal direction) andan initial size D2 along a second linear direction that is orthogonal tothe first direction (e.g., the lateral direction). In the fully expandedconfiguration (seen on the right in FIG. 3), portion 230 has anincreased size D3 in the first direction and an increased size D4 in thesecond direction. Thus, it is clear that the expansion of portion 230 isnot limited to expansion in the tensioning direction. Moreover, in someembodiments, the amount of expansion (e.g., the ratio of the final sizeto the initial size) may be approximately similar between the firstdirection and the second direction. In other words, in some cases,portion 230 may expand by the same relative amount in, for example, boththe longitudinal direction and the lateral direction. In contrast, someother kinds of structures and/or materials may contract in directionsorthogonal to the direction of applied tension.

In the exemplary embodiments shown in the figures, an auxetic structure,including an outsole comprised of an auxetic structure may be tensionedin the longitudinal direction or the lateral direction. However, thearrangement discussed here for auxetic structures comprised of aperturessurrounded by geometric portions provides a structure that can expandalong any first direction along which tension is applied, as well asalong a second direction that is orthogonal to the first direction.Moreover, it should be understood that the directions of expansion,namely the first direction and the second direction, may generally betangential to a surface of the auxetic structure. In particular, theauxetic structures discussed here may generally not expand substantiallyin a vertical direction that is associated with a thickness of theauxetic structure.

FIG. 4 is a top view of the side of outsole 320 that is not in contactwith the ground. FIG. 5 is a bottom view of the outsole of FIG. 4. ThusFIG. 5 is a view of the side of outsole 320 that is in direct contactwith the ground. Outsole 320 has a heel region 331, a midfoot or instepregion 332 and a forefoot region 333. In some embodiments, outsole 320may be comprised of an auxetic structure. As shown in these figures,outsole 320 bears a pattern of apertures 321 formed by a pattern oftriangular portions 322 that are joined at each of their vertices 323 tothe vertices of adjoining triangles. The combination of six triangles322 (depicted in dashed lines in the blow-out in FIG. 5) around each ofthe apertures 321 forms hexagonal patterns 324 (depicted in dash-dotlines in FIG. 5) as shown in FIG. 5.

As shown in FIG. 5, the hexagonal patterns vary in size and shape overthe length and width of the outsole. For example, the size of thehexagonal patterns is largest in the center 334 of the heel region 331and smallest at the instep region 337. For example, the distance fromone vertex of an aperture to an adjoining vertex of that aperture may betwice as great in the center of the heel region than at the instepregion of the sole. At the heel, in an exemplary embodiment, thereentrant angle for the side of the triangle that is generally orientedlaterally is quite shallow at about 150° to 170°, for example at 160°,whereas at the forefoot, that reentrant angle is much sharper, at about110° to 130°, for example at 120°. More generally, the reentrant anglesmay range from 100° to 170°. With this geometry, the auxetic structureat the heel expands in width under longitudinal tension to a greaterdegree than it expands in length when under lateral tension. At theforefoot, the reentrant angles do not differ as much, so that theexpansion in width under longitudinal tension at the forefoot is notthat much greater than the expansion in length under lateral tension.

In the example shown in FIGS. 4 and 5, the geometrical patterns formthrough-hole apertures 321, such that apertures 321 form holes all theway through the outsole 320. However, in other embodiments, outsole 320need not include through-hole apertures. Instead, outsole 320 mayinclude blind holes such that there is a thin continuous layer ofmaterial at the top or at the bottom of the outsole. In yet otherembodiments, the geometrical patterns may form through-holes in certainportions of the outsole and blind holes in other portions of theoutsole.

FIG. 6 is an enlarged views of the heel region 331, the midfoot region332 and the forefoot region 333, respectively, of the outsole shown inFIG. 5 when the outsole is not under tension. FIG. 6 shows that thehexagonal patterns formed by the combination of hinged triangles formingthe apertures in the central portion 334 of heel region 331 are largerthan the hexagonal patterns towards the lateral side 335 or the medialside 336 of heel region 331. For example, hexagonal pattern 351, whichis disposed in central portion 334, may be larger than hexagonal pattern353, which is disposed on medial side 336 of heel region 331. If theheel strikes the ground or playing surface in the direction that isnormal to the ground, triangular portions 322 in central portion 334 ofthe heel move towards the center of the hexagonal pattern 351. Thisincreases the density of the structure directly under the heel, andhelps cushion the impact of the heel striking the ground.

In the embodiment shown in FIG. 6, the hexagonal patterns in the centralportion 334 of the heel may be approximately symmetric with respect to alongitudinal axis that bisects the apertures 321 at the center of thehexagonal patterns. For example, aperture 342 is approximately symmetricwith respect to axis 390 that bisects aperture 342. The features in theadjoining columns of apertures on either side of the central portion 334of the heel, however, are not symmetric. For example, aperture 343 onthe medial side of the heel has a longer inwardly-directed portion 391than an outwardly-directed portion 392. Aperture 341 on the lateral sideof the heel also has a similar geometry, with an inwardly directedportion that is longer than an outwardly directed portion of aperture341. This geometry maximizes the ability of the central region tocompress and attenuate impact forces when the heel strikes the ground orplaying surface. In some embodiments, the dimensions of the features onthe lateral side 335 of the heel and on the medial side 336 of the heelare significantly smaller (for example, two-thirds the size or smaller)than the dimensions of the features at the center of the heel. Thesmaller dimensions of the hexagonal patterns on the lateral and medialsides of the heel allow the heel to maintain its curved shape around theupwardly curving contour of the heel, and maximizes the flexibility ofthe medial and lateral sides of the heel.

FIG. 7 is a cross-section taken at heel portion 331 shown in FIG. 6,showing an example of the construction of the footwear. In this example,the heel has three layers—an outsole layer 320, a midsole layer 340 andan insole layer 350. In some embodiments, outsole layer 320 is made of arelatively hard, abrasion resistant material, whereas midsole layer 340and insole layer 350 are made of relatively resilient materials so as toprovide a comfortable article of footwear. FIG. 7 also shows apertures321 through outsole layer 320 and midsole layer 340.

FIGS. 8-9 illustrates the auxetic characteristics of heel region 331 ofoutsole 320 as, for example, the wearer lands on the heel of thefootwear. Under longitudinal tension, heel region 331 increases inlength. However, because of the construction of outsole 320 as a patternof hinged triangles joined at their vertices, heel region 331 increasesin its lateral dimension as well (e.g., its width). For purposes ofillustration, the initial size of heel region 331 prior to applyingtension is indicated by line 371. This may help improve the tractionbetween the heel and the playing surface for various reasons. Forexample, because the ground-contacting surface is spread over a somewhatlarger area, this increases the likelihood that at least part of theheel will be in contact with a non-slippery playing surface when theheel hits the ground. Additionally, the openings between triangles allowthe triangles to expand, increasing the area of contact with the ground.Furthermore, the impact opens the inner edges of the triangularstar-shaped apertures so as to increase the engagement of the edges withthe playing surface.

FIG. 10 is another view of the heel region shown in FIG. 8. In thiscase, the heel region 331 has undergone lateral tension. For thatreason, the triangles have rotated and the dimensions of the heel region331 have increased longitudinally as well as laterally. The dashed line373 shows an outline of heel region 331 when it is not under tension.This configuration provides further improvements in traction when awearer cuts sharply or pushes off to one side or the other.

FIG. 11 is a schematic diagram of a sole showing apertures 321, formedby a pattern of triangular portions 322 that are joined to each other attheir vertices 323. In some embodiments, apertures 321 may becharacterized as triangular star-shaped apertures, due to the presenceof three star-like arms extending from a central region. However, aspreviously discussed, apertures 321 are not limited to particulargeometry, and could have any polygonal or non-polygonal geometry inother embodiments.

As noted above, the joints at the vertices function as hinges, allowingtriangular portions 322 to rotate with respect to each other as the solecomes under tension. Area 901 and area 902, denoted by the dashedcircles, are identified in FIG. 11 for further discussion with respectto FIGS. 12-14.

FIG. 12 is an expanded view of the area identified as 901 in FIG. 11,when the forefoot is under lateral tension. As shown in FIG. 12, whenthe forefoot is under lateral tension, for example when the wearer ispushing off to the side, the outsole at the forefoot increases indimension longitudinally as well as laterally, thus improving tractionwith the ground or playing surface. FIG. 13 is another expanded view ofthe area identified as 901 in FIG. 11, in this case illustrating theconfiguration of the sole when it is under longitudinal tension, forexample when the wearer is pushing off from his or her forefoot. FIG. 13shows that when the forefoot is under longitudinal tension, the outsoleincreases its lateral dimension as well as its longitudinal dimension.

FIG. 14 is an expanded view of the area identified as 902 in FIG. 11when the midfoot of the sole is under moderate longitudinal tension, forexample when the contact with the ground is transitioning from the heelto the forefoot. As shown in FIG. 14, when the midfoot of the sole isunder longitudinal tension, it increases in its lateral dimension aswell as in its longitudinal direction. FIG. 15 shows the midfoot when itis under even greater longitudinal tension, showing that the dimensionsof the sole have increased laterally as well as longitudinally to aneven greater extent.

FIG. 16 is an enlarged of the forefoot region 333 when the forefoot isin a rest condition and therefore not under tension. In the middleportion 381 of forefoot region 333, the outsole has larger hexagonalpatterns 324 on its medial side of the ball of the foot (i.e., where thephalange from the big toe meets a metatarsal bone), where a wearer wouldbe pushing off when making a sudden move to one side, and at the big toewhere a wearer would be pushing off to leap or run forwards. Theselarger features help absorb the impact of these moves, and increase thetraction of those regions of the outsole with the playing surface.

FIG. 17 shows the forefoot region of FIG. 16 when it is underlongitudinal tension, showing that the region under tension increasesits lateral dimension as well as its longitudinal dimension. FIG. 18shows the forefoot region of FIG. 16 when it is under lateral tension,showing that the region under tension increases its longitudinaldimensions as well as its lateral dimensions. As seen in FIGS. 17 and 18the auxetic structure of the outsole provides improved traction whensubjected to either longitudinal or lateral tension, since the overallsurface area of the outsole increases under either kind of tension.

FIGS. 19 to 25 illustrate an embodiment with a different sole structure.In this embodiment, sole 400 is made from an auxetic structure that doesnot appear to have openings when the structure is not under tension.However, this structure exhibits polygonal openings when the structureis under tension. Thus this structure can be described as being “closed”when it is not under tension (FIGS. 19 and 21), and “open” when it isunder longitudinal, lateral or other tension in the plane of thestructure (FIG. 22).

FIG. 20 is a side cross-sectional view of sole 400, showing treadpattern 410 on outsole 401 and midsole 402. In some embodiments, as seenin FIG. 20, outsole 401 may also include an outer covering 403. Theembodiment shown in FIGS. 19 to 25 has an outsole 401 made, for example,of a relatively hard material such as a hard rubber, and a midsole 402made of a relatively resilient material such as EVA foam or polyurethanefoam.

As shown in FIGS. 19, 21, 22 and 23, the outsole 401 and the midsole 402both have the auxetic structure described above, i.e., they have apattern of triangles joined at their vertices. The joints between thevertices 423 of triangles 422 are flexible, such that they function ashinges, allowing the triangles to rotate with respect to each other thusproducing the apertures 421 shown in FIG. 22 and FIG. 23.

The portion of the sole outlined in dark dashed lines 440 in FIG. 19 isshown in the four schematic diagrams of FIG. 23. These diagrams show howthe dimensions of the sole increase from their initial values when thesole is not under tension (the first diagram on the left) to when thesole is under low tension (second diagram), then when the sole is undermoderate tension (third diagram) and finally when the sole is undergreatest tension (fourth diagram).

FIG. 24 is a bottom view of an outsole of an embodiment shown in FIG. 19when it is not under tension. FIG. 24 identifies triangular feature 450and triangular feature 451 within dark dashed lines 440. FIG. 25 is asequence of four schematic diagrams showing how triangular feature 450and triangular feature 451 rotate away from each other and open theaperture 453 between them as the outsole undergoes increasing tension.

In the embodiment shown schematically in FIGS. 19 to 25, the outsole hasa tread pattern 410 that provides improved traction with the ground orthe playing surface. The outsole optionally also has a thin, elastic andflexible “skin” or outer covering 403 that is molded to fit over thetread pattern. This outer covering may be made, for example, from anelastomeric material. The outer covering may be used to prevent water,dirt, particulates or other debris from entering the triangular openingscreated when the sole is under tension.

The outer covering may be molded to fit into the star-shaped triangularapertures in the auxetic structure of the outsole. For example, FIGS.26-31 are schematic diagrams of an embodiment in which an elastic andflexible outer covering is molded to mate into the triangularstar-shaped openings of the auxetic structure. FIG. 26 shows the outsolestructure 501 when it is not under tension. Outsole structure 501 hastriangles 522 joined at their vertices 523 to adjoining triangles, whichare separated by apertures 521. When the sole structure is under tensionin one direction, it increases its dimension in that direction as wellas in the direction orthogonal to that direction and in the plane of thestructure, as shown in FIG. 27.

FIG. 28 is a schematic diagram of a top view of outer covering 503,i.e., it is a view from what would be the interior side of outercovering 503 when outer covering 503 is attached to the sole. Thisdiagram shows features 551 that protrude from the surface 550 of outercovering 503. FIG. 29 is a schematic diagram showing how outer covering503 mates with outsole 501. The features 551 on outer covering 503 arenow shown from the opposite side of outer covering 503, such that theyappear as recesses instead of protuberances. The outer covering (whichwould be on the bottom of an article of footwear and therefore bears theground-contacting surface) exhibits a triangular tread pattern 552.Because outer covering 503 is fabricated from a stretchable elasticmaterial, it stretches readily to accommodate the increased length andwidth of whatever portions of outsole 501 may be under tension. Thus thepattern of features 551 serves the dual function of mating to theauxetic material of outsole 501 and providing triangular tread pattern552 which serves to improve the wearer's traction against the playingsurface.

FIG. 30 is a side perspective view of a section of sole structure 500and outer covering 503, showing how the vertices in outer covering 503fit into apertures 521. Because outer covering 503 is made from a thin,flexible and elastic material, it can readily stretch to accommodate theexpansion of outsole structure 501 when it is under longitudinal orlateral tension. FIG. 31 is a cross-section of a portion of an exemplaryconstruction of sole structure 500, showing a midsole layer 530 and anoutsole layer 531, as well as outer covering 503.

FIGS. 32-38 illustrate another embodiment of an article of footwear 600with a sole having an auxetic structure that is light, flexible andcomfortable. This article of footwear is suitable for use as a shoe forlight jogging or walking. As shown in FIG. 32, this embodiment has anopen knit upper 601, an outsole 602 made of an auxetic structure, and aninsole 603. FIG. 32 shows that the polymer material forming outsole 602curves up around the back 631 of the heel 630 of the footwear, providingadditional reinforcement, support and protection at the back of theheel. As shown in FIG. 33 and FIG. 34, outsole 602 has a pattern ofreentrant triangular apertures 621 formed by the triangles 622 that arejoined at their vertices 623 to the vertices of other triangles. In thisembodiment, the size of reentrant triangular apertures 621 is relativelyuniform all over outsole 602. When a portion of footwear 600 is underlongitudinal or lateral tension due to an impact with the ground, thatportion of outsole expands in both directions, thus absorbing the impactand improving traction as described above. Outsole 602 may be made bymolding the auxetic structure shown in FIGS. 33-35 into a syntheticrubber, polyurethane or thermoplastic polyurethane material.

FIG. 35 is a schematic diagram of an enlarged view of the back 631 ofheel 630 of article of footwear 600. As shown in FIG. 35, the back 631of the heel 630 of upper 601 may be overlaid with the auxetic structureused for outsole 602 to strengthen the back of the heel. This may befabricated by overmolding the fabric of upper 601 with a polymer suchthat the polymer infiltrates and bonds with the material of upper 601.As shown in FIG. 35, the auxetic structure has reentrant angles at thebottom side of the apertures, such that the auxetic structure expandslaterally when it is under longitudinal tension. This effect facilitatespulling the shoe over the heel of the wearer's foot.

As best shown in FIG. 36 and also shown in FIG. 34, the flexibility offootwear 600 is enhanced by carve-out 650 at the instep region 604 ofoutsole 602. Carve-out 650 limits outsole 602 to just the lateral sideof the footwear at instep region 604, thus providing less resistance tothe upward bending of the heel with respect to the forefoot. Thisstructure provides a comfortable, low-stress article of footwear that isparticularly suitable for activities such as jogging or walking.

FIG. 37 is a schematic diagram showing that, in this embodiment, upper601 is sown to an insole 660 by stitching 661. Outsole 602 can then beattached to the bottom of insole 660 by using adhesives, for example, orby other means, such as by fusing, molding or stitching. FIG. 38 is across-section across a portion of the forefoot of article of footwear600 at as indicate in FIG. 33, showing insole 660, openings 621 andoutsole 602 as well as midsole 603, which is optional.

FIGS. 39-43 are schematic diagrams of an article of footwear 700 thatcould be used, for example, as a running shoe for running on hardsurfaces such as a paved road or an indoor track, where the runner wouldbe pounding the footwear against the ground. This embodiment has a wovenfabric upper 701 and a molded hard rubber or polyurethane outsole 702.

As shown in FIG. 40, outsole 702 bears a pattern of hexagonal patterns720 with reentrant triangular apertures 721 formed by triangles 722 thatare joined at their vertices 723 such that they function as hinges,allowing triangles 722 to rotate with respect to each other in responseto longitudinal or lateral tension. When any part of the outsole hitsthe ground or a playing surface, the vertical compression of the outsoleforces the triangles towards the center of the hexagonal patterns, i.e.,the triangular star-shaped apertures collapse towards their centers.This increases the density of the outsole in the area of impact, andattenuates the impact force. The pattern in outsole 702 may be formed bymolding the outsole material to form the pattern, or by cuttingtriangular star-shaped sections out of a solid material.

In this embodiment, the hexagonal patterns have roughly the same sizefrom the heel to the toe of the foot, with one hexagonal feature 741directly under the wearer's heel and several hexagonal patterns 743under the ball of the wearer's foot, as shown in FIG. 40. As best shownin FIG. 41, outsole 702 also has one hexagonal feature 742 directlyunder the wearer's big toe. Hexagonal patterns 720 towards the medial,lateral, front or rear portions of sole 702 curve upwards from theoutsole and are attached to the fabric of upper 701 by overmolding or byusing adhesives.

As shown in FIG. 42, the back 731 of the heel 730 of the upper 701 isreinforced with an overmolded or otherwise attached portion of hardrubber or polyurethane 750 bearing the hexagonal feature of a reentranttriangular aperture formed by triangles joined at their vertices. Whenthe footwear is pulled over the heel of the wearer's foot, the reentranttriangular aperture expands laterally, allowing the footwear to slipmore easily over the wear's heel. FIG. 39 and FIG. 42 show that portionsof the sole material may be molded over the fabric of upper 701,providing reinforcement and abrasion resistance to its lower edges.

FIG. 43 is a schematic diagram cross-section of the embodiment of FIG.40 taken at the forefoot, just in front of the laces as shown in FIG.40. This diagram shows outer sole 702 with apertures 721 attached to aresilient inner sole 703. Outer sole 702 may be attached to inner sole703 by using adhesives, overmolding or any other suitable means.

FIG. 44 is a schematic diagram of another embodiment of a shoe 800 thatcould be used for running or other sports or recreational activities.This shoe is generally similar to the shoe shown in FIG. 32, but it hasan additional peripheral band of material 810 connecting sole 802 toupper 801. Peripheral band 810 extends around the entire periphery ofsole 802 and upper 801. FIG. 45 is a schematic diagram of an interiorview of shoe 800 at its heel region 803, showing insole 820 attached tothe bottom edge of peripheral band 810 using stitching 821. The top edgeof peripheral band 810 is attached to the bottom edge of upper 801.Other methods of attaching peripheral bands 810 to the insole and to theupper may also be used. Peripheral band 810 provides additionalflexibility to footwear 800 by decoupling sole 802 from upper 801, thusallowing sole 802 to expand without being constrained by upper 801. Thepattern of apertures 830 in the midsole can be seen under insole 820.

The auxetic structures used for the outsoles and midsoles shown in thesefigures can be manufactured by molding a conventional polymer (such asEVA, rubber, polyurethane or thermoplastic polyurethane) to have thepattern of joined triangles or polygons with triangular or polygonalapertures as described herein. The structures could also be manufacturedby casting a solid polymer sheet and cutting the desired patterns intothe sheet. For example, the auxetic structure shown in FIGS. 4-15 may beproduced by molding a polymer to have the desired pattern, whereas theauxetic structure shown in FIGS. 16-19 may be produced by cutting thepatterns into a polymer sheet.

In some of the sole structures described above the whole extent of thesole is made of an auxetic structure. However, that is not a requirementfor all embodiments. For example, embodiments may use the auxeticstructure described above in any one, two or three of the heel region,the midfoot region and the forefoot region of the sole, or throughoutthe sole. The sole may have a single outsole layer. It may alternativelyhave an outsole and an inner sole, or an outsole, a midsole and an innersole, or an outer covering, an outsole, a midsole and an inner sole, orany combination of the above. It may have even more layers, as long asthe sole exhibits an auxetic structure such that, when under tension inone direction, it expands in the direction orthogonal to the directionof the tension.

The descriptions above have described auxetic structures using hexagonalpatterns formed of hinged triangles that have openings that increase inboth length and width when under longitudinal tension and also increasein both width and length when under lateral tension. These structurescould also be formed using auxetic foam material, which is a materialwith a negative Poisson's ratio, such that the resulting structureexpands in the direction orthogonal to an applied tension both becauseof its intrinsic properties and because the material itself isintrinsically auxetic.

The present embodiments depict auxetic structures that have asubstantial thickness in comparison to some other kinds of auxeticmaterials. Generally, the thickness of an auxetic structure, such as anoutsole comprising an auxetic structure, can vary. In some embodiments,an auxetic structure forming part of a sole structure may have athickness greater than or equal to a millimeter. In some embodiments, anauxetic structure can have a thickness greater than five millimeters. Insome embodiments, an auxetic structure can have a thickness greater thanten millimeters. In still other embodiments, the auxetic structure canhave a thickness greater than ten millimeters. Moreover, the thicknessof the auxetic structure can be selected in order to achieve desiredproperties such as cushioning and support.

In some embodiments, the thickness of an auxetic structure in a sole canbe used to enhance cushioning effects provided by the auxetic structure.FIGS. 46 and 47 illustrate how one or more apertures may change underapplied compressive forces, which may generally be applied in thevertical direction. When the outsole is compressed, for example when theoutsole hits the ground, the triangles tend to collapse towards thecenters of their respective triangular apertures, thus increasing thematerial within the region of impact, and further cushioning the impact.On the other hand, when a portion of the outsole is under tension, forexample when the wearer is pushing off from his or her forefoot, thatportion of the outsole expands in the lateral as well as in thelongitudinal direction, providing improved traction.

As seen in FIG. 46, with no compressive forces applied, apertures 920 ofa portion of an outsole 900 (shown schematically) may initially be open.However, as compressive forces are applied, as shown in FIG. 47,apertures 920 may close. This may generally occur because the triangularportions 922 that surround apertures 920 may tend to expand in sizeunder the compressive forces (due to mass conservation). This results inan inward contraction of apertures 920, which may have reduced openingsizes, or may completely close (as in FIG. 47). In particular,triangular portions 922 may be forced towards the centers of apertures920.

While various embodiments have been described, the description isintended to be exemplary, rather than limiting and it will be apparentto those of ordinary skill in the art that many more embodiments andimplementations are possible that are within the scope of theembodiments. Accordingly, the embodiments are not to be restrictedexcept in light of the attached claims and their equivalents. Also,various modifications and changes may be made within the scope of theattached claims.

What is claimed is:
 1. A sole structure for an article of footwear, thesole structure comprising: a midsole structure formed from anethylene-vinyl acetate or polyurethane foam and an outsole structure atleast partially formed from a rubber, the outsole structure including anoutsole layer and an outer covering disposed over the outsole layer, theouter covering including a ground-contacting surface disposed on oneside of the outer covering; wherein the sole structure has alongitudinal direction extending along a length of the article offootwear and a lateral direction extending along a width of the articleof footwear; wherein the longitudinal direction is tangential to theground-contacting surface of the outer covering and the lateraldirection is orthogonal to the longitudinal direction, wherein thelateral direction is also tangential to the ground-contacting surface ofthe outer covering; a plurality of apertures extending through athickness of the midsole structure and outsole layer, the plurality ofapertures being arranged in geometric patterns to form an auxeticstructure; wherein the auxetic structure is such that tensioning thesole structure in one of the longitudinal direction and the lateraldirection causes the outsole structure to expand in both thelongitudinal direction and the lateral direction; and wherein the outercovering extends across and into each of the plurality of apertures inboth of the midsole and the outsole to prevent water or debris fromentering the apertures, and wherein the outer covering is in contactwith a wall of each aperture.
 2. The sole structure according to claim1, wherein the outer covering comprises a stretchable elastic material.3. The sole structure according to claim 1, wherein the outer coveringincludes a plurality of features that protrude from theground-contacting surface and form protuberances on an opposite surfaceof the outer covering.
 4. An article of footwear comprising an upper anda sole structure attached to the upper, wherein the sole structure has alongitudinal direction extending along a length of the article offootwear and a lateral direction extending along a width of the articleof footwear, the longitudinal direction and the lateral directiondefining a plane, and wherein the sole structure comprises a compositeauxetic material, the composite auxetic material comprising: a firstlayer formed from a rubber, the first layer material comprising apattern of polygonal apertures surrounded by polygonal portions, whereineach polygonal portion is joined to an adjoining polygonal feature by aflexible joint such that the polygonal portions may rotate with respectto each other when the first layer is under tension; a second layerformed from an ethylene-vinyl acetate or polyurethane foam and attachedto the first layer, wherein the second layer has the same pattern ofpolygonal apertures as the first layer and wherein the pattern ofpolygonal apertures in the second layer is aligned with the pattern ofpolygonal apertures in the first layer; an outer covering of flexibleand elastic material attached to the first layer on a side of the firstlayer that is opposite to the second layer, wherein the outer coveringextends across and into each of the polygonal apertures in both thefirst layer and the second layer, and wherein the outer layer is incontact with a wall of each aperture; and wherein when the compositeauxetic material is under tension in a first direction, it expands inboth the first direction and in a second direction that is orthogonal tothe first direction.
 5. The article of footwear according to claim 4,wherein the outer covering is configured to stretch to accommodate theexpansion of the sole structure in the longitudinal direction and thelateral direction.
 6. The article of footwear according to claim 4,wherein the outer covering further comprises a triangular tread patterndisposed on a ground-contacting surface of the outer covering.
 7. Thearticle of footwear according to claim 4, wherein the composite auxeticmaterial further comprises a third layer of flexible and elasticmaterial attached to the second layer on a side of the second layer thatis opposite to the first layer, and wherein the third layer extendsacross each of the polygonal apertures in the second layer.
 8. Thearticle of footwear according to claim 4, wherein the outer coveringcomprises a pattern of polygonal features that protrude from its surfaceand that mate with the polygonal apertures in the first layer.